Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. (G • P) ? K, E ? Z, ~P ? ~ Z, G ? (E v L), therefore, (G • ~L) ? K (S v T) v E, S ? (F • ~G), A ? W, T ? ~W, therefore, (~E • A) ? ~G (S v T) v (U v W), therefore, (U v T) v (S v W) ~Q ? (L ? F), Q ? ~A, F ? B, L, therefore, ~A v B ~S ? (F ? L), F ? (L ? P), therefore, ~S ? (F ? P) In mathematics, it is very common for there to be multiple ways to solve a given a problem; the same can be said of logic. There is often a variety of ways to perform a natural deduction. In your peer responses, make suggestions for an alternate proof. Consider the following questions when constructing your response: If the proof was done using RAA, could it be done using CP? What about vice versa? Will a direct proof work for any of these? Can the proof be performed more efficiently by using different equivalence rules?